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Theorem ordeq 4890
Description: Equality theorem for the ordinal predicate. (Contributed by NM, 17-Sep-1993.)
Assertion
Ref Expression
ordeq

Proof of Theorem ordeq
StepHypRef Expression
1 treq 4551 . . 3
2 weeq2 4873 . . 3
31, 2anbi12d 710 . 2
4 df-ord 4886 . 2
5 df-ord 4886 . 2
63, 4, 53bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  Trwtr 4545   cep 4794  Wewwe 4842  Ordword 4882
This theorem is referenced by:  elong  4891  limeq  4895  ordelord  4905  ordun  4984  ordeleqon  6624  ordsuc  6649  ordzsl  6680  issmo  7038  issmo2  7039  smoeq  7040  smores  7042  smores2  7044  smodm2  7045  smoiso  7052  tfrlem8  7072  ordtypelem5  7968  ordtypelem7  7970  oicl  7975  oieu  7985
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886
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